13th International Conference on Membrane Computing - MTA Sztaki

<strong>13th</strong> <strong>International</strong> <strong>Conference</strong> on Membrane Computing, CMC13,
Budapest, Hungary, August 28 - 31, 2012. Proceedings, pages 115 - 124.
One-Membrane Symport P Systems with Few
Extra Symbols
Artiom Alhazov 1,2 and Yurii Rogozhin 2
1 Università degli Studi di Milano-Bicocca
Dipartimento di Informatica, Sistemistica e Comunicazione
Viale Sarca 336, 20126 Milano, Italy
E-mail: artiom.alhazov@unimib.it
2 Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
Academiei 5, Chişinău MD-2028 Moldova
E-mail: {artiom,rogozhin}@math.md
Abstract. Membrane systems (with symbol objects) are formal models
of distributed parallel multiset processing. Symport rules move multiple
objects to a neighboring region. It is known that for P systems with
symport rules of weight at most 3 and a single membrane, 7 superfluous
symbols are enough for computational completeness, and 1 is necessary.
We improve the lower bounds on the generative power of P systems with
symport of weight bounded by 3 and 4, in particular establishing that 6
and 2 extra symbols suffice, respectively.
1 Introduction
Membrane systems (with symbol objects) are formal models of distributed parallel
multiset processing. Symport rules move predefined groups objects to a
neighboring region [7]. In the maximally parallel mode (typical for membrane
computing), this alone is sufficient to construct a computationally universal device,
as long as the environment may contain an unbounded supply of some
objects. The number of symbols specified in a symport rule is called its weight.
The result of a computation is the total number of objects when the system
halts. In some cases, however, for technical reasons the desired result may only
be obtained alongside a small number of superfluous objects in the output region.
There were multiple papers improving the results on P systems with symport/antiport
of small weight (an antiport rule moves objects between 2 regions
in both directions, and its weight is the maximum of objects per direction), see
[5] for a survey of results. Computational completeness is achieved even for minimal
cooperation: either symport/antiport of weight 1, or symport of weight at
most 2. This holds for 2 membranes, without superfluous objects if the output is
considered in the skin, or with 1 superfluous object under the classical assumption
of the output in the elementary membrane. In the tissue case, the accepting
systems can even be made deterministic.
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